Weeks before his 1996 re-election, President Bill Clinton signed the Defense of Marriage Act, legally defining marriage as a union between a man and a woman. One of the law’s most dramatic consequences has been the deportation of members of same-sex binational couples—who, unlike members of heterosexual couples, cannot sponsor their foreign-born partners for a green card.

As Washington D.C.’s gay and lesbian news publication Metro Weekly reported on June 19, the Department of Justice’s Board of Immigration Appeals has delayed four cases involving same-sex binational couples while it investigates whether they would qualify as legally married should DOMA be found unconstitutional. If DOMA falls in court, the foreign individuals would be granted spousal green cards. (The Obama administration has pledged to no longer defend DOMA’s constitutionality in federal court, and it is likely that the law will soon be brought to the Supreme Court.)

For the couples affected by the BIA’s decision — all of whom are involved in a campaign titled“Stop The Deportations — The DOMA Project” — the news is a welcome surprise after years spent in what seemed a hopeless situation.

“For the first time, we have some sense that our family and our marriage really are taken with respect,” Frédéric Deloizy told Buzzfeed. Deloizy, who is French, married American Mark Himes in San Francisco in 2008 and lives in Harrisburg, Pa. with Himes and their four children.

When the BIA released its recent ruling, Deloizy was been preparing dinner for his kids when he got a call from his attorney, who was, as he puts it, “over the moon” about the decision. At first, Deloizy said, he wasn’t even sure what had happened; it took him a few seconds to realize the positive implications of the legal jargon he was hearing.

Himes and Deloizy met in Harrisburg at the birthday party of a mutual friend in 1990. They began dating soon after, and continued a cross-continental relationship until Deloizy moved to the states permanently in 1997, when he took a position teaching French at a Catholic high school in Harrisburg.

“I don’t even think we thought about DOMA in the very beginning,” Himes said. But the law suddenly became all-important when Deloizy lost his job in 2003. No longer a teacher, and unable to apply for a spousal green card, Deloizy could only remain in the United States legally if he obtained a student visa and began attending classes.

Himes and Deloizy believed the expense of tuition at a local community college — was worth taking on to ensure that the children they had recently adopted grew up in a home with two parents, but the bills were financially draining on a single income.

If the couple were to move to France, meanwhile, their four adopted children would not be legally recognized as French citizens.

Himes and Deloizy have in many ways become the face of “The DOMA Project” — they are featured in many of the articles written about the effort, and participated in “Through Thick and Thin,” a documentary about gay couples and immigration. Yet they consider themselves to be generally shy people.

“We are as boring as can be. We don’t want to be in the limelight,” Deloizy said. “But we have our kids.”

Tom Smeraldo and Emilio Ojeda, one of the four couples whose case was reviewed by the Board of Immigration Appeals.

On the other hand, Tom Smeraldo and Emilio Ojeda, whose case was also reviewed by the BIA, have long been vocal about gay rights and their opposition to DOMA.

“We always thought it was important to speak out, that somebody had to,” Smeraldo said. Smeraldo and Ojeda, too, were featured in “Through Thick and Thin,”

The couple met in a bar — “like most gay men of our age,” Ojeda said. This particular bar was called The Dugout, on Christopher Street in Manhattan’s West Village. At the time — the early 2000s — Ojeda, who had left Venezuela due to discrimination related to his sexual orientation, was working as a chef on a work sponsorship.

After a year though, he lost his job. However, when he applied for asylum the Immigration and Nationalization Service denied Ojeda’s request because he had not submitted his application within his first year of residence in the United States. Ojeda found himself entered into deportation proceedings, in danger of being required to return to Venezuela.

To keep Ojeda from needing to return to Venezuela, the two men ultimately decided to move to Canada, where they could become permanent residents and receive full spousal rights.

“I would call it self-deportation,” Smeraldo said. “Any other American man that is straight would not have to go through what we went through.”

The couple has an apartment in Toronto; Ojeda is working as a chef, and Smeraldo in Verizon’s international sales department.

But they miss the United States, especially Smeraldo’s family, who they haven’t seen in five years. “We would never have left the U.S. if we didn’t go through this,” Smeraldo emphasized. “I had a good life.” They want the option to return to the United States, to be reunited with Smeraldo’s family. So they continue fighting for Ojeda’s right to a green card.

It’s safe to say that especially for these individuals — the couples whose cases are being reviewed by the BIA —there’s a lot riding on November’s presidential election.

“Our only hope is Obama,” Smeraldo said matter-of-factly.

Yet even with the possibility of Obama’s re-election and the BIA’s decision — one that signals the possibility of a post-DOMA reality — they remain cautious.

“We would like to have the same rights, but honestly we have been in this situation for so long,” Deloizy said. “We don’t want to set our expectations too high because we don’t know what can happen.

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